Audit electrical power and energy

Follow energy as well as charge

Current conservation does not mean that no energy is transferred. A resistor dissipates electrical energy into its material while the steady current entering and leaving is equal. For a resistor with voltage drop V and current I, P = VI is power in watts (W), or joules per second. For constant power over a time t, transferred energy is E = Pt, in joules.

The browser’s energy column assumes 60 s at the selected steady settings. It is a prediction, not a timer or a measured heating experiment. The model has no temperature, heat capacity or cooling calculation.

Reconcile both circuit ledgers

At the default 6 V and R2 = 200 Ω, the series current is 0.020 A. R1 dissipates (2 V)(0.020 A) = 0.040 W; R2 dissipates (4 V)(0.020 A) = 0.080 W. Their sum, 0.120 W, equals source output (6 V)(0.020 A). In 60 s, the energies are 2.4 J and 4.8 J, totaling 7.2 J.

In parallel, R1 dissipates (6 V)(0.060 A) = 0.360 W and R2 dissipates (6 V)(0.030 A) = 0.180 W. Total 0.540 W agrees with (6 V)(0.090 A) from that circuit’s source. Energy in 60 s totals 32.4 J. These are different source outputs; the comparison does not hold source current or source power fixed.

Capture the default case and audit both ledgers before moving a slider. If a sum appears slightly different in another setting, use the calculation before rounding rather than adding only the three-decimal displayed values.

Say what is held fixed

Substituting Ohm’s law gives P = I²R = V²/R for an ohmic resistor. These equivalent expressions answer different controlled comparisons. At fixed current, larger resistance gives larger power. At fixed voltage, larger resistance gives smaller power. Neither sentence is complete without its fixed condition.

In the series default, the larger resistor has more power because both share current. In the parallel default, the smaller resistor has more power because both share voltage. Changing one resistance can also change the common current, so a before-and-after experiment needs the whole circuit recalculated.

At fixed resistances, doubling source voltage from 6 to 12 V doubles all currents and quadruples all powers. Predict the new total energies before checking: 28.8 J for series and 129.6 J for parallel over 60 s. Doubling time at fixed settings would instead double energy without changing power.

A component rating is not a predicted temperature

The model does not assign physical power ratings or predict whether a resistor survives. At 12 V, a 100 Ω parallel branch dissipates 1.44 W, which already exceeds a hypothetical 0.25 W component rating. A computed operating point is not permission to build it using arbitrary parts. Physical work needs an instructor-approved low-voltage, current-limited setup and components selected for the actual power; these examples are not mains-wiring instructions.

Transfer to a different duration

A 200 Ω ohmic resistor has a constant 4 V across it for 90 s. Calculate current, power, energy and transported charge. Check energy a second way using charge times voltage.

Check the power transfer

I = 4/200 = 0.020 A. P = 4 × 0.020 = 0.080 W. E = 0.080 × 90 = 7.2 J. Charge = 0.020 × 90 = 1.8 C. Then (1.8 C)(4 J/C) = 7.2 J, agreeing with the time-based calculation. A temperature rise cannot be calculated without additional thermal information.

OpenStax: electrical energy and power relates voltage, current and energy transfer. The browser comparison and transfer calculations are original examples.